[PPT] - Experiments to probe the pairing properties of double-beta decay PowerPoint Presentation

SLIDE 1

Experiments to probe the pairing properties of double-beta decay candidates.

Sean J Freeman

TRIUMF Workshop 2016

Speculations from an experimentalist point of view on pairing- related effects that might be important for 0νββ matrix element.

SLIDE 2

Pairing and 0νββ matrix elements.
Departures from BCS pairing.
Pair transfer reactions.
Review results of recent experiments:

76Ge-Se, 130Te-Xe and 100Mo-Ru.

What the literature says about:

150Nd-Sm, 136Xe-Ba and 82Se-Kr.

Some closing comments.

OUTLINE

SLIDE 3

Ga Ge As Br Kr Se

Mass Excess (MeV) Z β− β+/EC

Pairing is responsible for the viability of

double beta decay.

Smearing of the Fermi surface enables

2νββ in nuclei with a neutron excess, where it is otherwise Pauli blocked.

Conversion of two neutrons into protons –

should we expect pairing to be relevant to the matrix elements?

Pairing and Double Beta Decay

Some very basic connections between pairing and double beta decay:

SLIDE 4

!6# !4# !2# 0# 2# 4# 6# 8#

MGT(0ν)

48Ca 76Ge 82Se 130Te 136Xe

J=0 J>0

2

2 4 6 8 10 12 14 16

M

0ν (J)

5 lev. [gpp=1.90] M

0ν=1.37

7 lev. [gpp=1.04] M

0ν=3.41

13 lev. [gpp=0.83] M

0ν=3.82

128Te

J

1 2 3 4 5 6 7 8 9

If 0νββ NMEs are written as a sum over the angular momentum of the products of pair creation and annihilation operators, contributions from zero-spin pairs can be separated from other Jπ.

ˆ M (0ν) = X

Jπ

ˆ P †

Jπ

n ˆ

PJπ

p

Jπ

n

Jπ

p

Ubiquitous result: dominant contribution from J=0, but J>0 still significant and of opposite sign. Cancellation effects seem to diminish the long-range components, leaving a short range peak. A couple of recent examples:

SM: Caurier et al. PRL 100, 052503 (2008) QRPA: Escuderos et al. JPG 37, 125108 (2010)

Contributions to the GT matrix element with:

Pairing and Double Beta Decay

Šimkovic et al. PRC 79, 015502 (2009)

SLIDE 5

0νββ matrix elements as summation over states of different spins J in the A-2 nucleus.

76Se 76As 76Ge 74Ge

2 4 6 8 2 4 6

0+

2 4 6 8

summed 0νββ NME 0+ + 2+

2 4 6 8 10

all Jm

76Se − 74Ge − 76Ge

ν all

2 4 6

Ex in 74Ge (MeV) ν GT

2 4 6 8

(N all)/50

Pairing and Double Beta Decay

Brown et al. PRL 113, 262501 (2014)

NME dominated by the

contribution through the ground state.

Cancellations from

intermediate states with J>0.

Pairing enhances the J=0+

contribution.

Connection to pair

transfer reactions via complicated sums over quantities related to two- nucleon transfer amplitudes.

SLIDE 6

In shell-model treatments, more detailed set of interactions is used than simple pair correlations, albeit within a limited model space. In QRPA, pair correlations between like nucleons are treated separately from other effective interactions via the transformation to the quasiparticle regime within the Bardeen-Cooper-Schrieffer (BCS) approximation. BCS works well in many nuclei to describe pairing correlations for protons and neutrons, but there are some well-established nuclear structure scenarios where it fails.

Pairing in Different Nuclear Models Used for 0νββ

In IBM treatments, pairing implicit in the bosonisationapproach to truncating the model space.

SLIDE 7

Most important pair correlations are short-range correlations associated with J=0+ like nucleon pairs — good experimental probe is a reaction transferring two s-wave nucleons.

Yoshida first analysedreactions within a Born approximation:

Spectroscopic amplitudes for transfer of nucleon pairs from single-particle orbitals with j1 to those with j2 .
Between states with mixed single-particle configurations, summations in the amplitude over j1 and j2 .
Between BCS states, the summation is coherent due to common phase of amplitudes from different j values

— enhancements of the pair-transfer cross section.

Today, descriptions of the reaction mechanism are more sophisticated, but these essence of Yoshida’s insight remains.

Pair-Transfer Reactions

Yoshida NP 33, 685 (1961)

See for example, Potel et. al PRL 107, 092501 (2011)

Examples: (p,t)/(t,p) neutron and (3He,n) proton pair transfer reactions. Both t and 3He have a pair of s1/2 nucleons, with a strong overlap with pairs of correlated nucleons.

t p

SLIDE 8

Simple estimate (ignoring Q value effects):

σgs→gs σgs→2qp =  ∆ GU 2

ν

2 ∼ A 4 ∆ ∼ 12A−1/2 MeV G ∼ 28/A MeV U 2

ν ∼ 1

For medium-mass nuclei: transfer spectrum dominated by gs transition by factors of ∼30.

4

D. G. FLEMING

cd id.

For the 112Sn to lzoSn targets, no other states of significant strength appear in the range of excitation observed, which extends well above the pairing gap. Excited O+ states are characteristically the weakest on these targets, attaining, at most, only 3 y0

f the g.s. strengths. For the 122*r24Sn targets, however, several excited states of

llZ(P,l) g.s.(o+)

“%(p,t)

30”

.

.,“‘.

”

Fig. 1. Energy spectra of 20 MeV (p, t) reactions on targets of “%n,

ll*Sn, lz4Sn at a lab angle of 30”. The spectra have been adjusted so that the position of the r’sSn(p, t)“%n g.s. transition comes at the same place in each. The group of peaks occurring at 5 MeV excitation in the upper spectrum is due to a-leak through from the (p, a) reaction on the lz4Sn target. The energy resolution is 25 keV.

significant strength appear, although none in excess of 20 ‘A of the g.s. cross section; O+ states are again very weakly populated. Figs. 24 present the experimental angular distributions for the g.s. and lowest excited 2+ and 3- states for all the targets studied. The cross-section scales are in the same arbitrary units, although by comparing our

Excitation energy Fleming et al. NP A281, 389 (1977)

BCS Enhancement in Pair Transfer

isotopes were found to be the same within t 10 %_ We find essentially the same result for the (p, t> reaction on targets from A = 116 to A = 124, with some indication of a peaking at 122Sn/“20Sn, as can be seen in tables 1 and 2 and in fig. 2. The ‘9n(t, p) lzoSn g.s. transition was also observed to be the strongest one in ref. ““>. We note a decrease in the (114 + 112) g.s, cross section relative to the peak value which is outside the ex~~mental error of rf7 10 ‘A. This effect does not show up in the (t, p) data of ref. 24), but can be accounted for by DWBA calculations, which give slightly differing trends with mass for the (t, p) and (p, t) reactions at these energies.

TABLE 2

Experimental results for 20 MeV (p, t) reactions on tin 116, 114 and 112

116Sn(p, t)lr%n 114Sn(p, t)l%n 1i2Sn(g, t)‘rOSn D p.s. = --8.619f0.015

Q g.r. = -9.582ztO.020 Q *.a. = -10.485&0.015

“)

Ext. (MeV)
&O-50)

P

Ext. (MeV)

ur(fO-50) J=

Ext. (MeV)

u&O-50) .P

0.0

4300

+

0.0 ‘3300

+

0.0 1800

+

1.300i0.015 550 2” 1.250~0.015 340 2’ 1.215*0.0~0 1lOb) 2+ 2.200&0.015 130 4’ 2.35 130 3- 2.280~0.010 190 3- “) The mass excess of ll”Sn is found to be -85.820~0.018

MeV. All other Q-values were taken from

the compilation of Maples, Goth and Cemy (Nuclear Data Sheets, Vol. 2, Nos. 5 and 6, 1966). Our results are consistent with these values to within the errors shown, ‘) The cross section here is much more uncertain than the 115 % for the other 2” states, and could be in error by as much as A50 %.

The most striking result in the (p, t) data at 20 MeV is the ‘12Sn(p, t)““‘Sn g.s. cross

section. It is a factor of 2.5 weaker than the average of the A = 116-124 results. At

first sight, this result appears to be in direct conflict with the data of ref. ‘l). There, the (112 -+ 110) g.s. cross section relative to the (124 --) 122) transition is about three times stronger at 40 MeV than we observe at 20 MeV. The 20 MeV result can be readily seen in fig. 1. The ““‘Sn abundance is a factor of twenty greater than the abundan~s

f the other isotopes in the target and yet it has less than a factor of ten

increase in counts. Although this seeming discrepancy is dist~bing, such a difference is expected from DWBA calculations. We conclude then that, within the experimental errors, the g.s. transition strengths reported in refs. “* 24* 2 “) are consistent with results herein, when the differing reaction kinematics are taken into account.

4. Two-m&on

tramfer calculatims

4.1. BASIC THEORY OF TWO-NUCLEON TRANSFER REACTIONS

The general theory of 2NTR [ref. “‘)I and its extension to a pairing formal- ism 32-35) has been discussed extensively and will not be reproduced in any detail

112Sn(p,t) @ 30o

SLIDE 9

Breakdown in BCS: Pairing Vibrations

ε λ V2 ε λ V2

0+ BCS 0+ 0+

Strong pair transfer to gs. Other states at few % relative strength. Pair transfer associated with BCS state fragmented. Excited states with more significant strength. Gap larger than pairing energy Quantitative validity of BCS altered

SLIDE 10

Classical Example: N=126 Magic Gap

(p,t) (t,p)

Figure updated from Bohr and Mottelson Nuclear Structure Volume 2.

Large gap in neutron levels associated with N=126. Pair addition and removal creates pairing vibrations relative to 208Pb “vacuum”. If pairs are identical and interactions between them can be neglected harmonic spectrum results: Jπ=0+ states in Pb isotopes. Pairs below and above N=126: (n−2 ,n+2)

E = ~ω−2n−2 + ~ω2n2

Subshell gaps in spherical and Nilsson schemes also give rise to pairing vibrations.

SLIDE 11

Transitional Regions

At the onset of a deformed region, two-nucleon transfer from a “spherical” ground state to an excited 0+ “spherical” state in the residual nucleus, rather than the “deformed” ground state, can be significant due to the larger overlap in wave functions.

The classical example is relevant to 0νββ: [Generally more complicated since considerable shape mixing common in transitional regions.] A-2 A A-2 A A+2

1 3 2 Ex (MeV) 146 154 148 152 150 156 2Δ dσ/dΩmax (p,t) (t,p)

Samarium isotopes

N≈88-90 Sm nuclei are the classical example
f shape transition effects in pair transfer.
Population of excited 0+ states indicative of

changing shapes.

A likely issue for calculation of NME.

Bjerregaard NP 86, 145 (1966) Debenham NP A195, 385 (1972)

SLIDE 12

ββ: Removal of pair of neutrons and addition of a pair of protons: appears to be enhanced by pairing? (p,t): Removal of pair of neutrons. BCS enhancement of gs-gs. (3He,n): Addition of pair of protons. BCS enhancement of gs-gs.

Measurement of accurate cross sections might be useful as a check on ground-state wave functions.
If pairing vibrations are revealed by (p,t), (t,p) and (3He,n), BCS-correlations modified and fragmentation
f the pair transfer cross sections between 0+ states results from this more complicated structure.
Or indicates the possibility of changing shapes in a transitional region.

Consequences for Double Beta Decay?

76Se 76Ge 74Ge 78Se

ββ (p,t) (3He,t)

Q: Do these pair vibration phenomena arise in double beta decay candidates? IF they do: Q: Could there be some corresponding “fragmentation” of the decay probability? Q: What issues arise with on assuming BCS approximation in QRPA? Q: Do other models reproduce these structures?

SLIDE 13

Experimental Comments

10 20 30 40 0.01 0.05 0.10 Angle (deg.) σ (arb. units)

0+ (g.s.) 2+ (0.74)

(p,t): Fairly “routine” charged-particle spectroscopy. Dwindling facilities: Yale University (GONE!), RCNP Osaka University, IPN Orsay and Maier-Leibnitz Laboratory, Munich. (t,p): Fairly “routine” charged-particle spectroscopy. Troublesome radioactive beam in normal kinematics. Triton beams available 1970- 90; studies in the literature. (3He,n): “Troublesome” neutron time-of-flight spectroscopy. Dedicated facilities were available in the past; some recent work at Notre Dame University.

FOCAL PLANE TARGET UN-DEFLECTED TRAJECTORY POLE PIECE 2 POLE PIECE 1 COIL

$

Measure the energy spectrum of outgoing ions.
Identify 0+ states via forward peaked ℓ=0 transitions.
Measure cross sections accurately by minimizing

systematic effects.

Useful to make measurements on neighbouringisotopes

for consistency.

SLIDE 14

76Ge-Se: neutron pairing

1000 2000 3000 4000 1 10 100

Yield (gs normalised to 100)

1000 2000

Excitation Energy (keV)

1 10 100

76Ge 76Se

+ gs + gs +

* *

1000 2000 3000 4000 1 10 100 1000

74Ge

+ + gs +

(p,t) @ 3°

Excitation energy (keV) (σ/σgs)3◦ Ratio(3◦/22◦)

74Ge(p, t)72Ge

σgs(lab) = 6.4 mb/sr 100 86 691 29 280 834 2.8 0.9 1464 0.5 1.5 2024 0.5 4 2762 0.9 130

76Ge(p, t)74Ge

σgs(lab) = 6.7 mb/sr 100 50 596 3.2 1.0 1204 1.1 1.6 1463 2.2 0.8 2198 2.9 3 2833 1.7 6

76Se(p, t)74Se

σgs(lab) = 6.0 mb/sr 100 115 635 1.0 0.4 854 1.4 80

78Se(

)76Se (lab) = 7 1 mb/sr

Freeman al. PRC 75, 051301(2007)

Mordechai al. PRC 18, 2498 (1974)

MORDECHAI, FORTUNE, MIDDLETON,

AND

STEPHAN S

18 600-

E 400— E

K

LLI

I—

Z',

~ aoo-

CO CV CP tO Ol fly

Ge(t, p)

Ge

E(t}= 15 MeV

HL, b

= 18.75'

IO Ol gl Ill (A IO

+

0I

OP

Proton spectrum from the z4Ge(t, p)z&Ge reaction measured at 15

MeV incident energy and

at a laboratory

ingle of

18.75'.

The levels in Ge

are indicated

by their ex-

citation energies. Impurity groups are labeled accord-

ing to their residual nucle-

us.

60 70

PLATE POSITION

(cm)

80 the same set for the exit channel. An additional

set for the triton and the proton used in a recent Ge(p, t) work" was also examined.

No adjust-

ments of the latter triton set have been done since this potential was derived for the same mass region as the present work. The two potential

sets are listed in Table II.

Figure

2 shows

the angular

distributions for the

ground

sthte of "Ge and for two additional levels

bserved

with L = 0 transitions

in the present work.

'The solid curves are the DWBA calculations

using

Set (1,1) of Table II. The dashed curve drawn

with the ground

state angular distribution

repre-

sents the calculation

using Set (2, 2). It is clear that Set (1,1) is superior in fitting the ground

state angular distribution, especially

in the region of the second maximum.

Therefore, for all

the DWBA analysis

presented

below we chose

Set(1, 1). Figures

2 and 4 contain

the angular

dis-

tributions

characterized

by L = 2 and L = 4 angular momentum

transfer, respectively. Figure

5 pres-

ents the angular distributions characterized

by

dd L value.

Since no shell model wave functions were available for "Ge, we assumed pure configurations

for

the transferred neutron pair and therefore

no

attempt has been made

to compare the magnitudes

f the theoretical

and experimental

cross sections.

We have used the following configurations in the pWBA calculation:

(1g,@)2 for L= 0 and I.= 2 trans~

fers,

,(lg, ~~)' and (lg, ~m)' for L =4, (2P«„2d,@),

for L =1, (2p,~„2d,~,) for I, =2, and-(2p, », Ig,~~)

for L =5.

Table I summarizes

the excitation energies, the maximum

differential

cross section, L-value,

and spin and parity measured in the present study.

Also shown in Table I are the excitation energies

and J' values reported

in. the latest compilation. '

TABLE II. Optical-model parameters used in the analysis of the z4Ge(t, p)zeGe reaction. Set

Vp

(MeV)

1p

a

(fm) (MeV)

W'=4m~

(MeV)

a'

'Fp

(fm) (fm) (fm)

z46e+ t~

z4Ge+ tc

. z8Ge+ pa

z6Ge+ pc

'4oe + 2n

155b

170. 48.6 58.6

d

1,20

1.

17

1.

25

1.

12

1.

26

0.65 0.71 0.65 0.78 0.60 13.

5

25.3

1.

7

50.8

33.6

1.

60

1,

47

1.

25

1.

32

0.87 0.81 0.47 0.60

1.

3

1.

40

1.

25

1.

13 ~Reference 14.

Vp was adjusted to fit the first minimum

in the angular distribution for the ground state.

' Reference 11.

Adjusted to give a binding energy to each particle of 0.5[Q(t,p) +8.482] MeV.

Excitation energy 180μb/sr 76 μb/sr 3600 μb/sr

74Ge(t,p) @

19°

74Ge example of pairing vibration

due to shape coexistence.

In 0νββ candidates, excited 0+

states at the few % level.

SLIDE 15

76Ge-Se: neutron pairing

11
10
9
8
7

2 4 6 8 10 Q-value (MeV) σ3 deg.(mb/sr)

76Ge 76Se 74Ge 78Se

Experiment DWBA Becchetti DWBA Perey

No excited states in (p,t) or (t,p) > few % relative

to ground-state transition.

BCS for neutrons appears to be a reasonable

approximation.

Ground-state transitions are surprisingly

constant cross section.

Pairing in parent and daughter nuclei is

quantitatively similar.

Freeman al. PRC 75, 051301(2007)

SLIDE 16

76Ge-Se: proton pairing

2000 2500 3000 3500 4000 4500 180 200 220 240 260 280 300 320 Counts TOF (ns) (a)

74Ge(3He,n) 76Se

0.0 MeV

16O

4.1 MeV 10.0 MeV 7.0o 20.5o 1600 1800 2000 2200 2400 2600 180 200 220 240 260 280 300 320 Counts TOF (ns) (b)

76Ge(3He,n) 78Se

0.0 MeV

16O

10.0 MeV

50 100 150 200 250 300 350 400 5 10 15 20 25 dσ/dΩ (µb/sr) θc.m. (deg) (a)

74Ge(3He,n)

0+ calc. 2+ calc. Summed 50 100 150 200 250 300 5 10 15 20 25 θc.m. (deg) (b)

76Ge(3He,n)

Roberts al. PRC 87, 051305(2013)

No evidence for breaking of BCS approximation

for protons above the 5-7% level.

SLIDE 17

130Te-Xe: neutron pairing

100 101 102 103 1 2 3 4 100 101 102 103 0,ℓ= 0 666,ℓ= 2 2579,ℓ= 0 Counts per channel Excitation energy (MeV) 744,ℓ= 2 1873,ℓ= 0 2313,ℓ= 0

128Te(p,t)126Te

! = 5° 0,ℓ= 0

130Te(p,t)128Te

! = 5° ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ 1979,ℓ= 0 ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ 1 2 3 4 10–1 100 101 102 ℓ ℓ ℓ ℓ ℓ ℓ ℓ Te ℓ

132Xe(p,t)130Xe

θ = 5° 0,ℓ= 0 536,ℓ= 2 1794,ℓ= 0 2017,ℓ= 0 Excitation energy (MeV)

Contaminant

Bloxham al. PRC 82, 027308 (2007) Kay al. PRC 87, 011302 (2013)

Reaction E (MeV) σ (mb/sr) Ratioa Normalized strengthb

128Te(p,t)

4.21 90 1.21 1.873 0.06 20 0.02 2.579 0.15 21 0.04

130Te(p,t)

3.49 89 1.00 1.979 0.05 50 0.01 2.313(4)c 0.05 >20 0.01

For 130Te and 130Xe, again no signs of neutron pairing vibrations; excited 0+ states only weakly populated in (p,t). Experiments at Yale University, using a frozen Xe target.

SLIDE 18

130Te-Xe: proton pairing

800# 1000# 1200# 1400# 1600# 1800# 2000# 2200# 56# 60# 64# 68# 72#

2+ Energies (keV) Z/N Z=50 N=82

342

W . P . ALFORD et al .

285

410

295

420

285

410

~e :p(e) _ ° lTi1Ts-1~TfTC)2UDVYlB) '

Fig. 1 . Neut ron t ime-of - f l ight apoct ra at 0° . Ident i f ied levels not obvious at this angle are clear ly seen at

larger angles, e.g. the 3 .53 MeV level in '~°Xe.

The character ist ic smal l -angle peaking of the L = 0 t ransi t ions al lowed for thei r

easy ident i f icat ion in the data in spi te of the l imi ted resolut ion . Angular dist r ibut ions

which peak at angles between 0° and 20° are tentat ively ident i f ied as L = 2 or

L = 3 t ransi t ions . The max imum cross sect ions of levels populated in this study

are presented in table 2 .

3. DWBA analysis and mode l cakvlat ioo

Distor ted wave Born approximat ion (DWBA) calculat ions for compar ison wi th the exper imental ly measured angular dist r ibut ions were per formed using the computer code DWUCK4 5) . The 3He parameters are the B2 set taken f rom Becchet t i

et al . e) and the neut ron parameters are the "best f i t " set of Becchet t i and Greenlees ' ) .

These parameters, given in table 3, were chosen to be the same as those used for the

Cd( 3He, n)Sn react ion studies so that a di rect compar ison of cross sect ions .and

enhancement factors can be made between this and the previous studies. The cross

sect ions were calculated wi th a value Dô = 22 x 10° McV2 ~ fm3 for the zero-range

normal i zat ion factor . The proton binding energy is taken as one-hal f of the two- proton separat ion energy for the desi red state .

The exper imental and calculated cross sect ions are related by

200 300 300 ~Ti f °Fk.n) °~X° ~Ti ( ° l i °JJ°°Xs °°Te(°FI° ,n)~X°

E(~ie! " 254Md1 E(11e) " 2â4M°V

GS

E(SI~"25.4MN

GS

0 Deq

GS

0 Deq

0 D°q

b n

N

W

OI

+%
+%

.+% (+% ,+% ##+% #+% .+%

,0 /% 3.%4 3,/4 3!04 Z

C9 A. Z$ C"

Reaction E (MeV) σ (mb/sr) Ratioa Normalized strengthb

128Te(p,t)

4.21 90 1.21 1.873 0.06 20 0.02 2.579 0.15 21 0.04

130Te(p,t)

3.49 89 1.00 1.979 0.05 50 0.01 2.313(4)c 0.05 >20 0.01

128Te(3He,n)

0.24 – 0.96 2.13 0.095 – 0.32

130Te(3He,n)

0.26 – 1.00 1.85 0.098 – 0.34 2.49 0.062 – 0.21

a

Proton pairing vibration evident in (3He,n) spectra.
Associated with gap in proton single-particle levels at

Z=64.

Gap observed in other nuclear properties for protons.

Alford al. NP A323, 339 (1979)

SLIDE 19

Yield (arb.)

1 10

2

10

3

10

Ru(p,t)

102

1 10

2

10

3

10

Ru(p,t)

100

1 10

2

10

3

10

Mo(p,t)

100

Excitation energy (keV)

500 1000 1500 2000 2500 3000 3500

1 10

2

10

3

10

Mo(p,t)

98

1000 2000 3000

Excitation energy (keV)

10

1

10 10

1

!(6

)/!(15
)

102Ru(p,t) 100Ru(p,t) 100Mo(p,t) 98Mo(p,t)

100Mo-Ru: neutron pairing

J.S. Thomas et al. PRC 86, 047304 (2012)

Fragmentation of pair transfer strength: 20% to 735 keV in 98Mo.
Behavior asymmetric for (p,t) and (t,p).
Due to the onset of ground-state deformation in Mo isotopes

around A=100.

But clearly some shape mixing in the transitional region.

Systematics from (t,p)

Rahman et al. PRC 73, 054311 (2012) Transitions strengths normalised to 100Mo gs.

SLIDE 20

100Mo-Ru: neutron pairing

Similar transition happens at higher A in Ru.
For example, evidence in 102, 104Ru(t,p).
Parent and daughter nuclei in double beta decay

with differing deformations.

Although TOTAL pair removal strength consistent at

10% level.

130

H. W. FIELDING et al.

200[

'

' ' ' ' ' I ' . . . . . . . . I , , ,

'ZMo( SHe,rI)I4RLI

~0 deg G.S.

440

300[ ........ ~ ..........

i4Mo(SHe,n).Ru a.s.

210

CHANNEL NUMBER

I 420

2 0 , . , t . . , , . , . , , i . . . . . ,

"eMo(SHe,n)'SRu

8 deo

G.S.

f

260 470

2001 i ......... ~ .........

*°°Mo(SHe,n )aOZM u

6 dec 6.S.

l

Igo

60 ,

J

. . . . . ,,

, , ,

!°ZRu(~He.n)m4pd

deg

~,s.

I

480

400 CHANNEL NUMBER

585

Fig. 5. Time-of-flight spectra from targets of 92.94. 9e. x

OOMo and x O2Ru" Dispersion is approximately 0.2 ns per channel. Identity of prominent neutron groups is indicated.

4. DWBA analysis

The DWBA calculations were performed using the zero range code DWUCK4 1

).

The differential cross section for the reaction A(aHe, n)B can be written

db"2d° _ 8D 2 (½7¢A2)~ 2JB-I- 12JA_[_ l 2L-~-~ SAB (TAITA--I]TBTB)2(d-d-~)DW" (1)

The spin and isospin of the nuclear states are denoted by JA(MA), T^(T~) and

Ja(M~), TB(T~).

The rms radius of 3He, A, was assumed to be 1.7 fm.

100Mo-Ru: proton pairing

NEUTRON RICH ISOTOPES

NEUTRON RICH ISOTOPES 361

a sotid-state detector which monitored the elastic triton scattering at some convenient angle. I .OOL I\ I I I I I 4

‘04Ru ( t, p) ‘06Ru 3

Fig. 3. Measured angular distributions

for the lo4Ru(t, p) $06Ru reaction. The resufts are for states populated with L = 0 angular momentum transfers. The points are the data and the curves are DWBA fits as described in the text. The energies listed are excitation energies in keV. Figs. 3-6 show other distributions for states in “‘Ru.

Absolute cross-section scales were established in a separate experiment in which a counter telescope was used in conjunction with an SDS-930 on-line computer for particie identification 11> and the outgoing proton, deuteron and triton spectra were measured simultaneously. Elastic scattering cross sections were measured at small angles where they are expected to be from 85 to 100 % of Rutherford scattering and thus are insensitive to optical-model parameter uncertainties. The measured (t, t)

714μb/sr 135μb/sr 88μb/sr

Casten NP A184, 357 (1972) Fielding NP A269, 125 (1976)

Limited measurements of(3He,n).
Reaction on 100Mo does not appear to have evidence

for excited 0+ states in 102Ru, but less sensitive due to worse background and resolution of neutron time-of- flight spectroscopy.

SLIDE 21

150Nd-Sm: Neutron and Proton Pairing

1 3 2 Ex (MeV) 146 154 148 152 150 156 2Δ dσ/dΩmax (p,t) (t,p)

(t, p) REACTION 617 It is clear that on the basis of the present work alone, only J= = 0 + states can confidently be assigned from the shapes of the (t, p) angular distributions.

4.2. NUCLEAR STRUCTURE INFORMATION

The cross section for two-nucleon transfer reactions depends on the relative phases as well as on the amplitudes of the configurations which are present in the wave functions of the states excited 24). For this reason, in contrast to single-nucleon transfer reactions it is impossible to extract from the experimental cross section alone the details of the wave function. Indeed, nuclear model wave functions are a prerequi- site to the quantitative analysis of two-nucleon transfer reaction data. The absence

f such wave functions in the region presently under study, limits our interpretation
f the results to a qualitative one based on the general properties of these reactions.

Previous two-nucleon transfer studies of heavy nuclei have established that in regions free of gross structural changes most of the L = 0 strength in (t, p) reactions is concentrated in the ground state transition 6). The notable exceptions to this behaviour occur near major shell closures where pairing vibrations can be excited with appreciable strength zs) and near N = 90 in samarium where collective a

TM = 0 +

states and shape coexisting jR = 0+ states are excited with strengths comparable to the ground state 6). In fig. 9 we compare the J~ = 0 + states excited in the present Nd(t, p) studies with the results of the Sin(t, p) studies of Bjerregaard et al. 6). The overall trend in the neodymium case is similar to that of the samarium case, although there are also eeFtain differences which are worthy of comment. We discuss first the similarities. Both N = 84 nuclei show strongly (30 ~o of the

1,6

%-

ID

1.2 O.B 0.4

e, Nd

Srn

84 88 92 NEUTRON NUMBER

Fig. 9. Ratio of total L = 0 transition intensities for excited states below the energy gap to ground

state L ~ 0 intensity as a function of neutron number N for isotopes of neodymium and samarium.

N≈90 Sm nuclei are the classical example of shape transition effects

in pair transfer.

Nd nuclei show globally similar effects in (p,t) and (t,p), although

differs in the detail of the excited states.

148,150Nd(3He,n)150,152Sm does not populate excited 0+ states.

Sm Bjerregaard NP 86, 145 (1966), Debenham NP A195, 385 (1972) Nd Chapman NP A186, 603 (1972). Nd protons Alford NP A321, 45 (1979).

(t,p) Ratio of cross section of L=0 excited states to gs Neutron Number

SLIDE 22

136Xe-Ba: Neutron and Proton Pairing

Both targets are difficult, so not so well studied. But measurements on some neighboring nuclei reveal some interesting features.

142Nd, 140Ce and 132,134Ba(p,t): significant population of excited 0+ states. 136,138Ba(t,p): strong population of excited 0+ states around 3 MeV.

Point to neutron pairing vibrations associated with N=82, albeit with some fragmentation across several excited states. But pairing suppressed anyway. (3He,n) reaction on N=82 sees significant excited 0+ states, likely associated with the Z=64 subshell gap as in 130Te.

Alford al. NP A321, 45 (1979)

SLIDE 23

82Se-Kr

Some rudimentary (p,t) measurements on 82Se: difficult to

conclude much.

80,82Se(t,p) suggest significantly populated 0+ states below 1

MeV.

82,84Kr(p,t) performed, but only data/discussion of L=3

transitions in literature.

No measurements of (3He,n).

SLIDE 24

SYSTEM DATA COMMENTS

76Ge-Se

New data. BCS approximation good. Pairing similar across parent and daughter.

82Se-Kr

Sparse data: Se(t,p)

nly.

Difficult to be definitive, but some evidence of fragmentation in neutron pair removal.

100Mo-Ru

New (p,t) data. Fragmentation due to deformation, parent-daughter differences. Overall pairing looks similar across parent and daughter.

130Te-Xe

New (p,t) data. Neutron BCS approximation good. Proton pairing vibration associated with Z=64.

136Xe-Ba

Some relevant data available. Apparent influence of pairing vibrations associated with Z=64.

150Nd-Sm

Extensive data in literature Fragmentation due to deformation in neutron transfer.

Summary of experimental situation

Some evidence of breaking of BCS in ALL these cases, except for 76Ge-Se.

SLIDE 25

Summary:

In cases with pairing vibrations, there is a reduction in pair transfer strength between ground states. Does a similar reduction in strength occur for 0νββ? How much might it affect the decay rate? In these cases, what issues arise with the assumption of the BCS approximation in QRPA? Are these complicated aspects of nuclear structure reproduced in shell-model or IBM calculations? Would such a comparisons identify any useful physics for the matrix elements? Is there a quantitative connection between pair transfer strength and 0νββ that might be profitably pursued? To what extent do pairing correlations really matter for 0νββ?

SLIDE 26

To our many collaborators in Yale, Notre Dame and Munich experiments, and also to those who have contributed to the literature over the years. They were unlikely to have realised their data would contribute to this issue.

THANK YOU

Ge/Se(p,t): S.J. Freeman, J. P. Schiffer, A. C. C. Villari,

J. A. Clark, C. Deibel, S. Gros, A. Heinz, D. Hirata, C. L.

Jiang, B. P. Kay, A. Parikh, P. D. Parker, J. Qian, K. E. Rehm, X. D. Tang, V. Werner, and C. Wrede. Manchester, Argonne, GANIL, Yale, Open University. Ge/Se(3He,n): A. Roberts, A. M. Howard, J. J. Kolata,

A. N. Villano, F. D. Becchetti, P. A. DeYoung, M.

Febbraro, S. J. Freeman, B. P. Kay, S. A. McAllister, A.

J. Mitchell, J. P. Schiffer, J. S. Thomas, and R. O.

Torres-Isea Notre Dame, Minnesota, Michigan, Hope College, Manchester, York, Argonne. Mo/Ru(p,t): J. S. Thomas, S. J. Freeman, C. M. Deibel, T. Faestermann, R. Hertenberger, B. P. Kay, S. A. McAllister,

A. J. Mitchell, J. P. Schiffer, D. K. Sharp, and H.-F. Wirth

Manchester, Argonne, MSU, TU-Munich, MLL, Ludwig- Maximilians Munich, York. Xe/Te(p,t): T. Bloxham, B. P. Kay, J. P. Schiffer, J. A. Clark,

C. M. Deibel, S. J. Freeman, S. J. Freedman, A. M.

Howard, S. A. McAllister, P. D. Parker, D. K. Sharp, and J.

S. Thomas

Berkeley, Argonne, MSU, Manchester, York, Yale.